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<chapter style="counter-reset: chapter 9"><h1>Underactuated Manipulation</h1>
    
  <p>There is a lot more to manipulation than grasping!  The term
  <i>nonprehensile manipulation</i> means "manipulation without grasping", and
  humans do it often.  Pushing an object that is too big to grasp (e.g. an
  office chair) is a nice example, but we will see more subtle examples in this
  chapter, too.</p>
  
  <p>For force-closure-grasping manipulation, it is possible to think of a
  grasped object as effectively an extension of the distal links of the robot;
  the geometry and inertia of the manipuland effect the kinematics and dynamics
  of the robot, but as a control problem the manipuland does not contribute
  additional degrees of freedom to the problem.  Nonprehensile manipulation
  requires considering the additional (unactuated) degrees of freedom of the
  object.  This makes the entire control problem (controlling the degrees of
  freedom of the robot + the objects) an <a
  href="http://underactuated.mit.edu/">underactuated</a> control problem.  This chapter will focus on this very interesting class of control problems in the context of manipulation.</p>

  <p>Note that manipulation does not need to be nonprehensile to be underactuated.  As a nice example, Chavan-Dafle et al. considered the case were a two fingered gripper used external environmental contacts in order to perform in-hand re-orientation (see figure below), and referred to the task as "prehensile planar pushing"<elib>Chavan-Dafle20</elib>.  In this example, the grasp constrained the manipuland to the plane, but the external contacts were used to relocate and reorient the object within the grasp.</p>
    
  <figure>
    <img width="60%" src="data/chavan-dafle-prehensile-pushing.jpg"/>
    <figcaption>Prehensile planar pushing from <elib>Chavan-Dafle20</elib>; the robot exploits environmental contact to perform in-hand reorientation.  Images used with permission from Chavan-Dafle.  <a href="data/chavan-dafle-prehensile-pushing.gif">Click here to see the animated version.</a></figcaption>
  </figure>

  <section><h1>Model problems</h1></section>

  <section><h1>Planning through contact</h1></section>
  
  <section><h1>Visuo-motor policies</h1></section>

</chapter>
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